Question

A person starts walking 5 km north, then turns right and walks 3 km. Then turns right again and walks 5 km. Finally, he turns left and walks 2 km. How far is he from the starting point?

• A. 5 km
• B. 3 km
• C. 2 km
• D. 4 km

Hint:

For direction problems, use a coordinate plane with the starting point as (0,0). Track each move as a vector (x,y) based on direction (North: +y, East: +x, etc.). Sum the x and y components to find the final position, then calculate the straight-line distance using the distance formula: $\sqrt{x^2 + y^2}$. Draw a diagram to visualize the path and check for consistency.

Answer 1

The Correct Option is A

To solve the problem, we need to track the person's movements step-by-step and calculate the straight-line distance from the starting point to his final position.

1. Understanding the Concepts:

- Directions: North, East, South, West with turns affecting orientation.
- Displacement: The straight-line distance from start to end point.
- Use of Pythagoras Theorem: To calculate the distance in a right-angled triangle formed by movements in perpendicular directions.

2. Given Movements:

- Walk 5 km north.
- Turn right (east) and walk 3 km.
- Turn right again (south) and walk 5 km.
- Turn left (east) and walk 2 km.

3. Trace the Path:

- After first move: 5 km north.
- After second move: 3 km east.
- After third move: 5 km south → cancels out the 5 km north, so now at starting north-south level.
- After fourth move: 2 km east, so total east movement = 3 + 2 = 5 km.

4. Calculate Displacement:

North-south displacement = 0 km (since north 5 km and south 5 km cancel out).
East-west displacement = 5 km east.
Distance from start = 5 km.

Final Answer:

The person is 5 km away from the starting point.